I have to make a day trip to Osijek Croatia which is kind of located out of the way except the highway that crossed former Yugoslavia.. I 've got 3 options and all of them involve ground transportation. I was thinking about :
- Fly to ZAG and rent a car
- Fly to BUD and rent a car
- Fly to BEG and rent a car.

In last two options I will have to cross borders. Would rental car companies allow me to cross borders in these cases?

Are there better solutions?

I will have to do these on Zed fares and looks like BUD is the best airport in terms of number of flights as well..

Most of the time, yes. So long as you a returning the car to the same country they don't usually have any issue, however make sure you have all the paperwork you need to cross the border before leaving the rental desk.

The alternative would be to fly in, stop overnight and fly out again. Flights are operated by Croatia Airlines & Ryanair, but not more than one flight on any one day. Croatia operate to Split & Dubrovnik, and Ryanair to Hahn.

I would go to Zagreb and took a rental car ...just 2h with highway( toll is cca 100 kn or 20 usd ) and no borders...

Yes train is alternative and is cheap (one way is 120 kn or 24 usd )
for 10.7.2010
Zagreb......no.....Osijek......Travel time
06:55........783...11:28........04:33
07:35........983...12:47........05:12
09:58........703...14:30........04:32
12:57........981...18:30........05:33
16:57........581...21:12........04:15
18:20........551...21:48........03:28

Ryanair FRA-Hahn - Osijek ( Wed and Sun ) Osijek - FRA-Hahn
8.05............9.50..............................10.15.....12.00
and for me is to early if you are starting from Frankfurt-city ... but near FRA-Hahn you have small hotels for 40 eur/ night

BUD and BEG is only with renta car to Osijek ...another type of transport is a complicated and rare....

one more thing ...zag-osijek by bus is cca 4-5 h because they do not use the highway all the time ... no no no for me